1. **State the problem:** We need to find the average speed of the train over the entire journey from Manchester to Bournemouth, passing through London. 2. **Recall the formula for average speed:** $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$ 3. **Calculate total distance:** The train travels 210 miles from Manchester to London and 120 miles from London to Bournemouth. $$\text{Total distance} = 210 + 120 = 330 \text{ miles}$$ 4. **Calculate total time:** The train takes 3 hours for the first part and 2 hours for the second part. $$\text{Total time} = 3 + 2 = 5 \text{ hours}$$ 5. **Calculate average speed:** $$\text{Average speed} = \frac{330}{5} = 66 \text{ miles per hour}$$ 6. **Interpretation:** The train's average speed over the whole journey is 66 miles per hour.